### COLLOQUIUM - Brian Smith and "The Limits of the Subject in Badiou's 'Being and Event'"

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*comments*at the bottom of this post to view and join in the discussion.The paper given by Brian Smith of The University of Dundee on 'The Limits of the Subject in Badiou's

*Being and Event'*was an excillarating

*tour de force .*It brought both mathematics and philosophy into play, making a vital contribution at a time when Badiou studies is in its infancy in this country. The role of mathematics was introduced with its full force, something that philosophy really needs to feel today. Highly important points about how mathematics might respond to Badiou were developed and this took things beyond the philosophical response to Badiou and his use of mathematics.

This is a report of the paper and discussions at the 7th November Volcanic Lines Colloquium, the inaugural event of the Volcanic Lines: Deleuzian Research Group. We would like to thank our speaker for coming to Greenwich and delivering an extremely important and effective paper. The report is taken from my notes and I apologise for any errors or omissions.

The paper began with the birth of the subject and how the use of the axiom of choice brings this about. To explicate this much was made of the distinction between the two numbers systems in Cantor’s work on set theory: extensive or cardinal and intensive or ordinal. In addition the distinction between sets at a finite level and an infinite level was dramatised. Also explained was the nature and role of new infinite cardinal numbers through the distinction of a set’s elements and its subsets. Using the whiteboard set theoretical axioms and proofs were elucidated, including the distinction between belonging and inclusion, allowing for a subset to be included but not belong. The point was made that set theory allows Badiou to talk not in terms of wholes and parts but about inclusion and belonging, establishing yet another fundamental distinction. Returning to the generation of cardinal numbers the move was made to the power set. This was explained as the way in which set theory allows us to get more out of sets by applying certain rules.

The divergence between the two number systems at the infinite level was shown in the variation of the intensive, or that with intrinsic order, whilst the cardinal stays the same. The extensive remains the same while the intensive and structural varies. This for Badiou provides us with the complexity of presentation. The divergence of cardinal and ordinal at the infinite level was explained by the repetition of the operation of 'taking the limit' so as to increase complexity. The question was then raised – is the mathematics of the infinite controllable? The set was clarified as that whose beginning or foundation can be found but which has no end so that where it goes is open. Its beginning is finite but where it is going is not. Cantor’s major problem was elaborated at this point – the undecideable or indeterminate greatness of the power set. For Cantor this must be avoided. To do this he asserts his continuum hypothesis, leading to strict determination and a closed system. The direction Badiou is taking was brought out here because he wants to keep the system open. The move to non-constructible sets concerns what is bigger than what is constructible. This introduces the chance and randomness of unordered sets that inflates infinite levels.

A point that I found particularly striking was that mathematics involves operations that happen all at once or immediately whilst Badiou’s appropriation of mathematics adds a historical structure or temporality. Historical situations (as opposed to natural situations) need a temporal dimension and this calls upon a set whose elements are non-constructible sets. The empty set was then opposed to a foundational set. This, it was emphasised, depended upon Badiou’s situated and temporal appropriation of set theory. Therefore the matheme of the event is not a set we find in mathematics but an inconsistent set. This set belongs to itself and is therefore inconsistent. The continuum hypothesis favoured by Cantor fails in an inconsistent situation and this, according to Badiou, is 'experienced' in this situation. The temporal dimension was developed in terms of the need of the individual to be fully realised as a subject, subject-hood not being given in advance but made a task.

The temporal extension of set theory proceeds via decision or the affirmation of an event. The point was made that this introduced pure chance at the infinite level alongside strict order that can be applied to anything through pure choice (the Axiom of Choice). This combination of freedom and determinism was emphasised. Next the nature of problems in Badiou’s system was developed as creative and novel, requiring a new situation in which to deal with them. Yet, to be more precise, in this move the subject extends the situation but doesn’t create a new one because such a creating would make the subject transcendent to the situation.

Also touched on were things that the speaker found to be haunting Badiou’s system. Deeply interesting and fertile were concluding remarks on the of set theory: ‘There are so many clearly defined bizarre entities within this universe [of set theory] that many of the aspects of philosophy that Badiou wants to reject, especially in recent continental philosophy, can return from the realm of inconsistency, where he banishes them, and associate themselves with some of these more unusual and offbeat products of mathematics.’ The independence of the Axiom of Choice could reintroduce themes of the Other and the sublime. This was explored in the question session in terms of an event which is encountered as something beyond the ‘free rational power to manage’ of the subject. The irrational returns in a ‘self destructive subject’, with fidelity to something beyond reason’s control.

The question session grappled with some fundamental issues brought out by the paper. Badiou’s concern with changing the world, with action, was emphasised. Subjective response to the undecidable event is truth and not knowledge. Set theory shows the immanent extension of the situation so that the problem is affirmed in this new situation. The problem then doesn’t disappear as if it were a lack of knowledge removed by attaining knowledge. This of course resonates with Deleuze’s notion of problems – something the ‘Clamour of Being Reading Group is likely to engage with over the next four weeks at Greenwich and online. The speaker dealt with concerns that Badiou fails to engage with what known by emphasising that truth is distinct from knowledge and that this must be understood through set theory.

A questioner raised the point that chaos in the universe is an important concern for contemporary thought. The speaker linked this to historical temporality with the subject transforming a situation.

The issue of Badiou’s apparent anthropocentricism was raised. Notions of rationality and the potential of a rational individual, distinguished in this way from animals, were discussed. There is no event without a subject and no subject without an event.

The problem of an event that does not come from an evental site was raised in terms of Lacan’s eruption of the Real, a terrifying rupturing of the symbolic network. The speaker emphasised that the event has to be, for Badiou, the starting point of production, something to be taken up by subject. Time then is a succession of events and the truth procedures that carry on from them. The speaker then developed his argument that Badiou’s system or model can involve the event going too far, overwhelming the subject. The axiom of choice means that the subject needs to be able to deal with every event. This, he argued, is the limit of the subject in Badiou’s Being and Event.

The discussion then moved to the simulacrum as it figures in Badiou’s thinking. The speakers critique of Badiou was further explored – showing its depth and challenge. A questioner raised the subject of the Holocaust, asking whether fidelity to this (as if to an event) is a case of evil for Badiou? The speaker raised the problem that a very subjective like structure results from the Holocaust, and he had explained that for Badiou the definition of ethics is ‘to be subjective’. The simulacrum looks like a subject but the event has gone wrong. The speaker argued that this is still a subject according to Badiou’s model, an unintended consequence.

A questioner raised the issue of the religious connotations of the word evil. The speaker considered Badiou’s use of the terms good and evil as deliberately provocative but not religious.

Next a question raised the rarity of the event in Badiou and the notion that we are all rational individuals that inhabit a situation, with freedom in the form of the axiom of choice, but are not all subjects. The speaker puts this in the context of Badiou’s appropriation of set theory which itself gives no reason for the rareness of events. From this he concluded that it is a question of how Badiou applies set theory if we want to find a reason for the rareness of events.

The final question asked about Badiou’s engagement with political conventions like voting. The speaker sketched Badiou’s development from his earlier anti-statist stance to his later concern with the subject involved in the transformation of a state. The questioner was concerned with engagement, with Badiou’s relevance to parliamentary democracy. The point was again made that a concern with knowledge must be contrasted with Badiou’s concern with truth. Concern with maintaining a state would preclude fidelity to an event.

The paper had set out and explained fundamental distinctions in Badiou’s Being and Event and drew out the consequences and difficulties these give rise to. The role of mathematics was brought out in a much needed way. It leaves us a thinking about both the need to engage with the complexity of the system and to consider ‘the limits of the subject.’ We must engage fully and rigorously and in this way arrive at any critical responses we might want to make. In terms of the forthcoming reading group on Badiou’s ‘Deleuze: The Clamour of Being’ we now have an invaluable insight into the specific concerns that animate his reading and critique of Deleuze. It should allow Badiou to play a full role when his encounter with Deleuze is staged, our speaker having given much life to him through a thorough elucidation, appreciation and critical assessment.

**Please feel free to continue the discussion by clicking**

*comments*below this post. A window will open - select*other*if you are not signed up with blogger.Labels: axiom of choice, badiou, being and event, event, mathematics, politics, subject, the limit

## 3 Comments:

The paper by Brian is published at 'Cosmos and history' for those who are interested.

First of all I would like to thank Brian Smith for a very interesting talk. I have small question about the use of mathematics in philosophy. In his Deleuze-book Badiou says somewhere that he insists that Deleuze is using mathematics (calculus, differential topology) only in a metaphorical way. Can we consider Badiou's integration of mathematics and philosophy as non-metaphorical, and what does he mean exactly with metaphorical?

I think we should definitely pursue this question during the reading group. It makes me think about pages 220-221 of Difference and Repetition. Here Deleuze talks about the mathematico-biological system of different/ciation. He says that mathematics and biology ‘… appear here only in the guise of technical models which allow the exposition of the virtual and the process of actualisation, along with the exploration of the two halves of difference,…’ I don’t know if Badiou refers to this passage but it seems relevant to this question. If Deleuze’s use of mathematics is metaphorical perhaps it is in the sense that maths appear to be a way of describing or talking about and exploring the actual-virtual production mechanism which is not literally applicable to it. For Badiou maths must be ontology itself. The question I suppose is whether for Deleuze maths is metaphor which allows us to model something else or whether it is actually operating in the process of different/ciation and only captured progressively by mathematics. Certainly, earlier in chapter 4 of Difference and Repetition the differential equation is associated with ‘the universal and its appearance’ (p. 171). This tension between maths providing a universal operation in this production and the need to keep open the terms in which this production is to be talked about or modelled is a problem.

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